[uni level stats] confidence intervals and stats
So if I have 158 samples, 21 positive, 126 negative and 11 invalid.
I have no false positives or false negatives so the sensitivity,specificity and accuracy is 100%.
How do I work out the confidence intervals and sd etc?
Any help would be appreciated:)
To calculate confidence intervals and standard deviation for your sample data, you can follow these steps:
Step 1: Calculate the proportions:
- Calculate the proportion of positive samples (p) by dividing the number of positive samples (21) by the total number of samples (158).
- Calculate the proportion of negative samples (q) by dividing the number of negative samples (126) by the total number of samples (158).
Step 2: Calculate the standard error (SE):
- The standard error measures the variability or uncertainty in the proportion estimate. It is calculated using the formula: SE = √(p*q/n), where n is the sample size (158).
Step 3: Calculate the confidence interval (CI):
- The confidence interval provides a range of values within which the true population proportion is likely to fall. It is based on the standard error and a chosen level of confidence.
- A commonly used confidence level is 95%. To calculate the 95% confidence interval, you can use the formula: CI = p ± (Z * SE), where Z is the Z-score associated with the chosen confidence level.
- For a 95% confidence level, the Z-score is approximately 1.96.
Step 4: Calculate the standard deviation (SD):
- The standard deviation provides a measure of the dispersion of the data.
- In this case, since you have a binary outcome (positive/negative), you can use the formula: SD = √(p*q).
So, to summarize:
- Calculate p = 21/158 = 0.133.
- Calculate q = 126/158 = 0.797.
- Calculate SE = √(p*q/n).
- Calculate CI = p ± (1.96 * SE).
- Calculate SD = √(p*q).
Please note that these calculations assume that your sample is representative of the population you are studying.